Related papers: Pfaffian Schur processes and last passage percolat…

We study line ensembles arising naturally in symmetrized/half-space geometric last passage percolation (LPP) on the $N \times N$ square. The weights of the model are geometrically distributed with parameter $q^2$ off the diagonal and $cq$…

In this note we provide a short proof of the distributional equality between last passage percolation with geometric weights along a general down-right path and Schur processes. We do this in both the full-space and half-space settings, and…

In this note we give a(nother) combinatorial proof of an old result of Baik--Rains: that for appropriately considered independent geometric weights, the generating series for last passage percolation polymers in a $2n \times n \times n$…

Last passage percolation (LPP) in an $n\times n$ lower triangular domain has nice connections with various generalizations of Schur measures. LPP along an anti-diagonal, from $(1,n)$ to $(n,1)$, gives a distribution of a highest column of a…

We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the origin to the point $\big(n,n^{\lfloor a…

We derive Sasamoto's Fredholm determinant formula for the Tracy-Widom GOE distribution, as well as the one-point marginal distribution of the ${\rm Airy}_{2\to1}$ process, originally derived by Borodin-Ferrari-Sasamoto, as scaling limits of…

We study the two-time distribution in directed last passage percolation with geometric weights in the first quadrant. We compute the scaling limit and show that it is given by a contour integral of a Fredholm determinant.

This article studies several properties of the half-space last passage percolation, in particular the two-time covariance. We show that, when the two end-points are at small macroscopic distance, then the first order correction to the…

We study fluctuations of the current at the boundary for the half space asymmetric simple exclusion process (ASEP) and the height function of the half space six vertex model at the boundary at large times. We establish a phase transition…

In this paper we will prove a shape theorem for the last passage percolation model on a two dimensional $F$-compound Poisson process, called the Hammersley model with random weights. We will also provide diffusive upper bounds for shape…

We prove a GUE central limit theorem for random variables with finite fourth moment. We apply this theorem to prove that the directed first and last passage percolation problems in thin rectangles exhibit universal fluctuations given by the…

For exponential last passage percolation on the plane we analyse the probability that the point-to-line geodesic exhibits an atypically large transversal fluctuation at the endpoint as well as the probability that the point-to-point…

We study the Facilitated TASEP, an interacting particle system on the one dimensional integer lattice. We prove that starting from step initial condition, the position of the rightmost particle has Tracy Widom GSE statistics on a cube root…

We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one-point distribution of the geodesic location joint with the last passage times, and its limit as the parameters go to…

The one-dimensional polynuclear growth model with external sources at edges is studied. The height fluctuation at the origin is known to be given by either the Gaussian, the GUE Tracy-Widom distribution, or certain distributions called…

This note establishes a universal directed landscape limit for last passage percolation models in an intermediate scaling regime. We find as a quick consequence the transversal fluctuations for geodesics taken near the axis. We extend the…

We study a symmetrized (half-space) version of geometric last passage percolation with a boundary parameter $c$ that interpolates between subcritical, critical, and supercritical behavior. This model gives rise to a family of interlacing…

We consider the first passage percolation model on the square lattice. In this model, $\{t(e): e{an edge of}{\bf Z}^2 \}$ is an independent identically distributed family with a common distribution $F$. We denote by $T({\bf 0}, v)$ the…

We prove that the rescaled one-point fluctuations of the boundary of the percolation cluster in the Bernoulli-Exponential first passage percolation around the diagonal converge to a new family of distributions. The limit law is indexed by…

We consider the exactly solvable model of exponential directed last passage percolation on $\mathbb{Z}^2$ in the large deviation regime. Conditional on the upper tail large deviation event $\mathcal{U}_{\delta}:=\{T_{n}\geq (4+\delta)n\}$…